This invention relates to digital compensation of a non-linear circuit or system, for instance linearizing a non-linear power amplifier and radio transmitter chain with a multi-band input, and in particular to effective parameterization of a digital pre-distorter used for digital compensation.
One method for compensation of such a non-linear circuit is to “pre-distort” (or “pre-invert”) the input. For example, an ideal circuit outputs a desired signal u[.] unchanged (or purely scaled or modulated), such that y[.]=u[.], while the actual non-linear circuit has an input-output transformation y[.]=F(u[.]), where the notation y[.] denotes a discrete time signal. A compensation component is introduced before the non-linear circuit that transforms the input u[.], which represents the desired output, to a predistorted input v[.] according to a transformation v[.]=C(u[.]). Then this predistorted input is passed through the non-linear circuit, yielding y[.]=F(v[.]). The functional form and selectable parameters values that specify the transformation C( ) are chosen such that y[.]≈u[.] as closely as possible in a particular sense (e.g., minimizing mean squared error), thereby linearizing the operation of tandem arrangement of the pre-distorter and the non-linear circuit as well as possible.
In some examples, the DPD performs the transformation of the desired signal u[.] to the input y[.] by using delay elements to form a set of delayed versions of the desired signal (up to a maximum delay τP), and then using a non-linear polynomial function of those delayed inputs. In some examples, the non-linear function is a Volterra series:y[n]=x0+ΣpΣτ1, . . . ,τpxp(τ1, . . . τp)Πj=1 . . . pu[n−τj]ory[n]=x0+ΣpΣτ1, . . . ,τ2p-1xp(τ1, . . . τp)Πj=1 . . . pu[n−τj]Πj=p+1 . . . 2p-1u[n−τj]*In some examples, the non-linear function uses a reduced set of Volterra terms or a delay polynomial:y[n]=x0+ΣpΣτxp(τ)u[n−τj]|u[n−τ|(p-1).In these cases, the particular compensation function C is determined by the values of the numerical configuration parameters xp.
In the case of a radio transmitter, the desired input u[.] may be a complex discrete time baseband signal of a transmit band, and y[.] may represent that transmit band as modulated to the carrier frequency of the radio transmitter by the function F( ) that represents the radio transmit chain. That is, the radio transmitter may modulate and amplify the input v[.] to a (real continuous-time) radio frequency signal p(.) which when demodulated back to baseband, limited to the transmit band and sampled, is represented by y[.].
There is a need for a pre-distorter with a form that both accurately compensates for the non-linearities of the transmit chain, and that imposes as few computation requirements in terms of arithmetic operations to be performed to pre-distort a signal and in terms of the storage requirements of values of the configuration parameters. There is also a need for the form of the pre-distorter to be robust to variation in the parameter values and/or to variation of the characteristics of the transmit chain so that performance degradation of pre-distortion does not exceed that which may be commensurate with the degree of such variation.
In some systems, the input to a radio transmit chain is made up of separate channels occupying distinct frequency bands, generally with frequency regions separating those bands in which no transmission is desired. In such a situation, linearization of the circuit (e.g., the power amplifier) has the dual purpose of improving the linearity of the system in search of the distinct frequency bands, and reducing unwanted emissions between the bands. For example, interaction between the bands resulting from intermodulation distortion may cause such unwanted emission.
One approach to linearizing a, system with a multi-band input is essentially to ignore the multi-band nature of the input. However, such an approach may require substantial computation resources, and require representation of the input signal and predistorted signal at a high sampling rate in order to capture the non-linear interactions between bands. Another approach is to linearize each band independently. However, ignoring the interaction between bands generally yields poor results. Some approaches have relaxed the independent linearization of each band by adapting coefficients of non-linear functions (e.g., polynomials) based on more than one band. However, there remains a need for improved multi-band linearization and/or reduced computation associated with such linearization.